Kinematic Wave Models of Network Vehicular Traffic

The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are expected to be theoretically rigorous, numerically reliable, and computationally efficient. For traffic systems with inhomogeneous links, merges, diverges, or mixed-type vehicles, we study the kinematic waves in their Riemann solutions and develop numerical solution methods of the Godunov type and the supply-demand type. For a network traffic system, we propose a multi-commodity kinematic wave (MCKW) model and an implementation of it. The model observes First-In-First-Out principle in the order of a time interval and is numerically convergent. Further, we apply this simulation model to study equilibrium states and periodic waves in road networks. Finally, we summarize our work and discuss future research directions.Comment: Ph.D. Dissertation. UC Davis. 218 pages, 12 tables, 61 figure

Linearized Reconstruction for Diffuse Optical Spectroscopic Imaging

In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows recovering the diffusion coefficient and absorption coefficient simultaneously, provided that their spectral profiles are incoherent and a sufficient number of wavelengths are judiciously taken for the measurements. We also discuss the reconstruction for imperfectly known boundary and show that with the multi-wavelength data, the method can reduce the influence of modelling errors and still recover the absorption coefficient. Extensive numerical experiments are presented to support our analysis.Comment: 18 pages, 7 figure

ℓ1\ell_1-minimization method for link flow correction

A computational method, based on $\ell_1$-minimization, is proposed for the problem of link flow correction, when the available traffic flow data on many links in a road network are inconsistent with respect to the flow conservation law. Without extra information, the problem is generally ill-posed when a large portion of the link sensors are unhealthy. It is possible, however, to correct the corrupted link flows \textit{accurately} with the proposed method under a recoverability condition if there are only a few bad sensors which are located at certain links. We analytically identify the links that are robust to miscounts and relate them to the geometric structure of the traffic network by introducing the recoverability concept and an algorithm for computing it. The recoverability condition for corrupted links is simply the associated recoverability being greater than 1. In a more realistic setting, besides the unhealthy link sensors, small measurement noises may be present at the other sensors. Under the same recoverability condition, our method guarantees to give an estimated traffic flow fairly close to the ground-truth data and leads to a bound for the correction error. Both synthetic and real-world examples are provided to demonstrate the effectiveness of the proposed method

A New Approach to Calculating Dynamic Pricing of High-Occupancy-Toll (HOT) Lanes Can Improve the Performance of Travel Corridors

There are two operational objectives for optimizing the operation of HOT lanes: (i) maintain free-flow conditions on HOT lanes and (ii) move as many vehicles as possible through HOT lanes to minimize the travel corridor’s total delay. Meeting these objectives will help guarantee trip time reliability of both HOVs and paying SOVs and minimize congestion on general purpose (GP) lanes. The key factor in achieving these objectives is the price charged to SOVs, which determines the percentage of SOVs choosing to use the HOT lanes. This in turn requires operators to adjust the toll fee in response to changing levels of traffic congestion. However, achieving these goals efficiently is contingent upon dynamic pricing strategies where tolls are adjusted in real time in response to traffic levels to maximize the total throughput while preventing queuing on the HOT lanes

The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency dependence, as is often seen in biological tissues. We discuss reconstruction methods for both fully known and partially known spectral profiles, and demonstrate in the latter case the successful employment of difference imaging. We also study the reconstruction with an imperfectly known boundary, and show that the multifrequency approach can eliminate modeling errors and recover almost all inclusions. In addition, we develop an efficient group sparse recovery algorithm for the robust solution of related linear inverse problems. Several numerical simulations are presented to illustrate and validate the approach.Comment: 25 pp, 11 figure

Real-Time Misbehavior Detection in IEEE 802.11e Based WLANs

The Enhanced Distributed Channel Access (EDCA) specification in the IEEE 802.11e standard supports heterogeneous backoff parameters and arbitration inter-frame space (AIFS), which makes a selfish node easy to manipulate these parameters and misbehave. In this case, the network-wide fairness cannot be achieved any longer. Many existing misbehavior detectors, primarily designed for legacy IEEE 802.11 networks, become inapplicable in such a heterogeneous network configuration. In this paper, we propose a novel real-time hybrid-share (HS) misbehavior detector for IEEE 802.11e based wireless local area networks (WLANs). The detector keeps updating its state based on every successful transmission and makes detection decisions by comparing its state with a threshold. We develop mathematical analysis of the detector performance in terms of both false positive rate and average detection rate. Numerical results show that the proposed detector can effectively detect both contention window based and AIFS based misbehavior with only a short detection window.Comment: Accepted to IEEE Globecom 201